MinT - Best Known (39, 39+45, s)-Nets in Base 5

Best Known (39, 39+45, s)-Nets in Base 5

(39, 39+45, 78)-Net over F₅ — Constructive and digital

Digital (39, 84, 78)-net over F₅, using

t-expansion [i] based on digital (38, 84, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(39, 39+45, 965)-Net in Base 5 — Upper bound on s

There is no (39, 84, 966)-net in base 5, because

1 times m-reduction [i] would yield (39, 83, 966)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10473 657552 802434 378820 452378 278572 851011 408882 251020 937025 > 5⁸³ [i]